login
A131597
Bigomega of Pisano periods mod n, i.e., number of prime divisors (counted with multiplicity) of the period of Fibonacci residues mod n.
0
0, 1, 3, 2, 3, 4, 4, 3, 4, 4, 2, 4, 3, 5, 4, 4, 4, 4, 3, 4, 4, 3, 5, 4, 4, 4, 5, 5, 2, 5, 3, 5, 4, 4, 5, 4, 3, 3, 4, 4, 4, 5, 4, 3, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 3, 5, 5, 3, 2, 5, 4, 3, 5, 6, 4, 5, 4, 4, 5, 6, 3, 4, 3, 4, 5, 3, 5, 5, 3, 5, 6, 5, 5, 5, 5, 5, 4, 4, 3, 5, 5, 5, 5, 6, 5, 5, 4, 6, 5, 5, 3, 5, 5, 4, 5
OFFSET
1,3
COMMENTS
The Pisano sequence (A001175) is not known exactly for all n. It is known that Pisano(n) <= 6n, Pisano(10) = 60, etc. (see A001175). In addition, Pisano(m) is even if m > 2, and Pisano(m) = m iff m = 24*5^(k-1) for some integer k > 1. Bigomega seems an interesting function of Pisano(n).
LINKS
Eric Weisstein's World of Mathematics, Pisano period.
Wikipedia, Pisano period.
FORMULA
a(n) = A001222(A001175(n)).
EXAMPLE
F(mod 5): 0 1 1 2 3 0 3 3 1 4 0 4 4 3 2 0 2 2 4 1 0 1 1 ...
period = 20; bigomega = 3 (since 20 = 2*2*5).
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Finley (pfinley(AT)touro.edu), Aug 30 2007
STATUS
approved